Existence of fuzzy prekernels and Mas-Colell bargaining sets in TU games

10.1142/s0219198907001369 ◽

2007 ◽

Vol 09 (02) ◽

pp. 199-213 ◽

Cited By ~ 2

Author(s):

MARC MEERTENS ◽

J. A. M. POTTERS ◽

J. H. REIJNIERSE

Keyword(s):

Bargaining Set ◽

Tu Games ◽

The Core ◽

Symmetric Games ◽

Bargaining Sets ◽

Additional Assumptions

The paper investigates under which additional assumptions the bargaining set, the reactive bargaining set or the semireactive bargaining set coincides with the core on the class of symmetric TU-games. Furthermore, we give an example which illustrates that the property 'the bargaining set coincides with the core' is not a prosperity property.

ON BARGAINING BASED POINT SOLUTION TO COOPERATIVE TU GAMES

10.1142/s0219198907001461 ◽

2007 ◽

Vol 09 (02) ◽

pp. 361-374 ◽

Cited By ~ 1

Author(s):

V. THANGARAJ ◽

A. SUGUMARAN ◽

AMIT K. BISWAS

Keyword(s):

Grand Coalition ◽

Payoff Vector ◽

Tu Games ◽

Single Imputation ◽

Coalition Structures ◽

Side Payments ◽

Cooperative Tu Games ◽

Shapely Value ◽

Point Solution ◽

Consider the cooperative coalition games with side payments. Bargaining sets are calculated for all possible coalition structures to obtain a collection of imputations rather than single imputation. Our aim is to obtain a single payoff vector, which is acceptable by all players of the game under grand coalition. Though Shapely value is a single imputation, it is based on fair divisions rather than bargaining considerations. So, we present a method to obtain a single imputation based on bargaining considerations.

Proceedings of the 2015 International Industrial Informatics and Computer Engineering Conference ◽

A New Theorem on Bargaining Sets in TU Games

10.2991/iiicec-15.2015.149 ◽

2015 ◽

Author(s):

Wenbo Yang ◽

Jiuqiang Liu

Keyword(s):

Tu Games ◽

Reactive and Semi-Reactive Bargaining Sets for Games with Restricted Cooperation

10.1142/s0219198920500012 ◽

2020 ◽

Vol 22 (03) ◽

pp. 2050001

Author(s):

Natalia Naumova

Keyword(s):

Sufficient Conditions ◽

Existence Results ◽

Simple Games ◽

Bargaining Set ◽

Tu Games ◽

Restricted Cooperation ◽

Generalized Kernel ◽

Existence Conditions ◽

Necessary And Sufficient ◽

Generalizations of reactive and semi-reactive bargaining sets of TU games are defined for the case when objections and counter-objections are permitted not between singletons but between elements of a family of coalitions [Formula: see text] and can use coalitions from [Formula: see text]. Necessary and sufficient conditions on [Formula: see text], [Formula: see text] that ensure existence results for generalizations of the reactive bargaining set and of the semi-reactive barganing set at each TU game [Formula: see text] with nonnegative values are obtained. The existence conditions for the generalized reactive bargaining set do not coincide with existence conditions for the generalized kernel and coincide with conditions for the generalized semi-reactive bargaining set only if [Formula: see text] and [Formula: see text]. The conditions for the generalized semi-reactive bargaining set coincide with conditions for the generalized classical bargaining set that were described in the previous papers of the author. For monotonic [Formula: see text], the condition on [Formula: see text] for existence of the generalized semi-reactive bargaining sets on the class of games with nonnegative values is also necessary and sufficient on the class of simple games, but similar result for the generalized classical bargaining sets is proved only for [Formula: see text].

On Bargaining Sets of Convex NTU Games

10.1142/s0219198915500085 ◽

2015 ◽

Vol 17 (04) ◽

pp. 1550008 ◽

Cited By ~ 1

Author(s):

Bezalel Peleg ◽

Peter Sudhölter

Keyword(s):

Bargaining Set ◽

Ntu Games ◽

The Core ◽

Ntu Game ◽

We show that the Aumann–Davis–Maschler bargaining set and the Mas-Colell bargaining set of a non-leveled NTU game that is either ordinal convex or coalition merge convex coincides with the core of the game. Moreover, we show by means of an example that the foregoing statement may not be valid if the NTU game is marginal convex.

THE RIVER SHARING PROBLEM: A SURVEY

10.1142/s0219198913400161 ◽

2013 ◽

Vol 15 (03) ◽

pp. 1340016 ◽

Cited By ~ 10

Author(s):

SYLVAIN BEAL ◽

AMANDINE GHINTRAN ◽

ERIC REMILA ◽

PHILIPPE SOLAL

Keyword(s):

Optimal Allocation ◽

Market Mechanism ◽

Tu Game ◽

Tu Games ◽

Cooperative Tu Game ◽

Fair Distribution

The river sharing problem deals with the fair distribution of welfare resulting from the optimal allocation of water among a set of riparian agents. Ambec and Sprumont [Sharing a river, J. Econ. Theor. 107, 453–462] address this problem by modeling it as a cooperative TU-game on the set of riparian agents. Solutions to that problem are reviewed in this article. These solutions are obtained via an axiomatic study on the class of river TU-games or via a market mechanism.